As a lifetime horse lover and enthusiast, maybe some of my experience may be interesting. Many girls of all stripes and types enjoy interacting with horses so I don't think autism "causes" horse obsession. On the other hand many facets of horse-friendly environments may match our ND needs. For instance,
1. Horses are 'cuddly'. The gentle ones are large, warm, strong, enjoy predictable strong touch. Grooming a horse (and they need a lot of this) requires lots of slow, repetitive, routine motion. And, if you like the smell of horses, horse odor can be really meditative and calming.
2. As prey animals, horses do better in a quiet, predictable environments. They usually don't like loud noises, things that fly and flap around, vibrations, unfamiliar places, new foods. They have meltdowns, need time to chill out, and never try to explain what's going on to you. They can be kindred spirits, cohabiting autistic-comfortable places.
3. Horses are honest, intuitive, patient, and don't ask questions or require that you speak to them. After school it was such a relief to escape to the stable, groom, saddle and bridle my horse, and go for a long solitary ride through the woods on his back. He didn't care if I sang, made funny noises (not too loud), talked to the squirrels, or was just silent. We shared a lot of safe-unsafe attitudes but no rules about right and wrong or judgements about disability, being odd or acting crazy. With a horse you are who and what you are.
Most of my life I was lucky enough to be able to be near live, friendly horses, to own them, ride and show them. But the idea of horses also captivated me. I read about them, drew them, collected horse figurines, and pretended to be them throughout my childhood. I've read about non-verbal autistic children being able to communicate with other humans through an intermediate object like a toy or a computer. Perhaps horses serve that purpose for some ND kids. A shared love of horses gave me a point of connection to people I otherwise felt no commonality with. The criticism I got from my riding instructor would have sent me away in tears had I not been able to share the responsibility for failure with my horse. Kids who wouldn't speak to me in the classroom would happily include me on the playground if I was pretending to be a horse.
I'll bet people with other obsessions and hobbies have similar experiences. Maybe it's motorcycles or fly tying that creates a meeting ground and lets those who are usually divided by their differences find a shared space to peacefully co-exist together for a while...